Translational partition function

statistical mechanics, the translational partition function, $q_{T}$ is that part of the partition function resulting from the movement (translation) of the center of mass. For a single atom or molecule in a low pressure gas,  neglecting the interactions of molecules, the Canonical Ensemble $q_{T}$ can be approximated by:

$q_{T}={\frac {V}{\Lambda ^{3}}}\,$ where $\Lambda ={\frac {h}{\sqrt {2\pi mk_{B}T}}}$

Here, V is the volume of the container holding the molecule, Λ is the Thermal de Broglie wavelength, h is the Planck constant, m is the mass of a molecule, k_B is the Boltzmann constant and T is the absolute temperature. This approximation is valid as long as Λ is much less than any dimension of the volume the atom or molecule is in. Since [[Thermal de </math>

The factor of N! arises from the restriction of allowed N particle states due to Quantum exchange symmetry. Most substances form liquids or solids at temperatures much higher than when this approximation breaks down significantly.

See also

• Rotational partition function
• Vibrational partition function
• Partition function (mathematics)